Dynamic Asset Allocation - Stanford University
Dynamic Asset Allocation
Using Stochastic Programming and Stochastic Dynamic Programming Techniques
Gerd Infanger
Stanford University
Winter 2011/2012
MS&E348/Infanger
1
Outline
? Motivation ? Background and Concepts ? Risk Aversion ? Applying Stochastic Dynamic Programming
? Superiority of Dynamic Strategies
? Applying Multi-Stage Stochastic Programming ? Summary
Winter 2011/2012
MS&E348/Infanger
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Asset Allocation
? Allocation between asset classes accounts for the major part of return and risk of a portfolio
? Equity investments ? Interest-bearing investments
? Selection of individual instruments is a lower-level decision with much smaller influence on portfolio performance
? Asset Allocation should consider all financial aspects
? Current and future wealth, income, and financial needs ? Financial goals ? Liquidity (plan for the unexpected)
? Financial industry suggests that investors need customized investment strategies
Winter 2011/2012
MS&E348/Infanger
3
Typical Financial Advice
? Questionnaires to assess the risk aversion of an investor
? (E*Trade, Charles Schwab, Fidelity, Financial Engines, ASI, etc...) ? Taking measure, often with great sophistication and much detail ? => risk aversion of the investor (typically assuming constant relative risk
aversion, CRRA)
? Choose from standardized portfolios:
? Conservative, e.g., 20% stocks ? Dynamic, e.g., 40% stocks ? Progressive, e.g., 60% stocks
? Is that a customized portfolio?
Winter 2011/2012
MS&E348/Infanger
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Financial Advice (cont.)
? More recently life-cycle funds have emerged
? E.g., Fidelity Freedom 2020 ? Asset allocation is purely time-dependent
? Often practiced rule of thumb: % stocks = 100 ? age ? But these strategies do not depend on wealth, expected performance,
cash flow, etc.
Winter 2011/2012
MS&E348/Infanger
5
Multi-Period Investment
Asset classes
Returns process
Stocks Bonds
Cash
W0
W1
W2
t=0
t=1
t=2
(Network formulation based on John Mulvey (1989))
Winter 2011/2012
MS&E348/Infanger
WT Max u (WT)
6
Utility
? A utility function is an integrating measure, assigning a value (utility) to each point (possible outcome) of the distribution of returns or wealth.
? Maximizing expected utility is equivalent to choosing a certain distribution (of return or wealth) from all possible obtainable distributions.
? Risk measures, like mean, standard deviation, Sharpe ratio, downside risk, value at risk, etc., are all quantities describing various aspects of a distribution.
Winter 2011/2012
MS&E348/Infanger
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Dynamic Asset Allocation
? In real life investors change their asset allocation as time goes on and new information becomes available.
? In theory investors value wealth at the end of the planning horizon (and along the way) using a specific utility function and maximize expected utility.
? Fixed-mix strategies are optimal only under certain conditions. ? In general and in most practical cases the optimal investment strategy
is dynamic and reflects real-life behavior.
Winter 2011/2012
MS&E348/Infanger
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